A few GMAT questions - 1

Question

Hi All,

I will be posting sets of questions every now and then. Here are the first in line:

1. If a,b,c,d are in continued proportion then (a-d)/(b-c)>=x. Find the value of x?

2. In order to maintain the price line, a trader allows a discount of 10% on the marked price of the goods in the shop. However, he still makes a gross profit of 17% on the cost price. Find the profit percent he would have made on the selling price had he sold at the marked price?

3. There are 3 taps A,B,C in a tank. They can fill the tank in 10, 20 and 25hrs respectively. At first all of them are opened simultaneously. Then after 2 hours tap C is closed and A and B are kept running. After the 4th hour tap B is also closed. The remaining work is done by tap A alone. Find the percentage of work done by tap A itself?

4. Ram and Shyam run a race of 2000m. First Ram give Shyam a start of 200m and beats him by 30sec. Next, Ram gives Shyam a start of 3 min and is beaten by 1000m. Find the time in which they can complete the race seperately?

5. At a game of billiards, A can give B 15 points in 60 and A can give C 20 in 60. How many points can B give C in a game of 90?

quangviet512 · Answer

2.I f sold at the marked price so the profit must be (17%*90%+10%)/100% = 25.3%

3.The percentage of work B and C done is 2*1/25+4*1/20=7/25
So A did 18/25 of work

4.We call the pace of them are R and S so
2000/R=1800/S+0.5
1000/R=2000/S-3
So we have 2000/R=8000/1375mins ; 2000/S=65/11mins

mikki0000 · Answer

1. If a,b,c,d are in  continued proportion  then

What does continued proportion mean? 

In addition, I don't understand q5. Is the 60 and ninety time? What does "giving" 15 points mean??

MG

prashrash · Answer

I am getting all different answers! Don't know if the method I am following is correct or not .. pls correct me if i am wrong.

Problem 2:
Let marked price = x
then selling price = 0.9x
now, SP - profit = CP ---- (i)
also, it is stated that profit is 17% of the cost. hence,
profit/CP*100 = 17%
=> P = 0.17CP
Substituting this in (i),
0.9x - 0.17CP = CP
=> CP = 0.9x/1.17 ----- (ii)

If product was sold at marked price, then SP = x
Profit = SP - CP = x - 0.9x/1.17
hence, profit over cost would be
(1 - 0.9/1.17)/(0.9/1.17) * 100 = 30%

Problem 3:
The question asks what percentage of work does A do alone . If we follow the formula 1 - (2/25 + 4/20), we obtain what amount of work A has done in overall, which will also include the work that A did in conjunction with B and C. This is not what is asked.
Soln:
A, B, C work together for first 2 hrs. So amt of work done =
2*(1/10+1/20+1/25) = 19/50.
Work remaining = 1 - 19/50 = 31/50
A and B work together for the next 2 hours. So amt of work done =
2*(1/10+1/20) = 3/10
Work remaining = 31/50 - 3/10 = 16/50
Now, this work was done by A alone
So %age effort by A alone =
(16/50)/1 * 100 (since we assume 1 to be the total amount of work initially)
= 32%

Problem 4:
let R and S be the speeds of Ram and Shyam resp. Their speeds will always remain same.
From 1st statement:
Let x be the time taken by Ram to finish the race,
then, R = 2000/x --- (i)
and S = 1800/(x+30) --- (ii)
from stmt 2:
Let b be the time taken for Ram to come to the 1000m mark
R = 1000/b --- (iii)
S = 2000/(b+180) ( 3 minute lead) --- (iv)

Equating (i) and (iii), we get x = 2b
Equating (ii) and (iv), and solving we obtain the value of x and b as
b = 120 sec
x = 240 sec
thus R takes 4 mins to complete the race (directly obtained from (i))
S takes 120+180 = 300 sec = 5min to complete the race (directly obtained from (iv))

Not sure abt problems 1 and 5.. in problem 5 there is no relation given between B and C. How do we assume how many points B can give C ? B can give all points it has to C!! :-)

prashrash · Answer

in problem 1, I am assuming continued proportion to mean a/b=b/c=c/d. But not getting ideas even from there

prashrash · Answer

in problem 2, the q asks profit on selling price and not on cost.
Thus %age profit =  /x * 100
= 23% approx.

Apologies for the oversight.

yessuresh · Answer

I guess the answer for Question 5 is 54
A/B = 45/15
A/C = 40/20
Then B/C = 2/3. If total is 90 then B gives C 54.

abba_rv · Answer

Answers for the questions:
1. 3 (I really do not know how to do this!!)

2. 23% (Already solved)

3. (18/25)*100 (prashrash - the question asked is what is total percentage of work done by A..u have considered only the last segment)

4. 4, 5 (this was easy)

5. 10 (Again, if I anybody can solve this it will be great...cldnt decipher it myself!)

A few GMAT questions - 1

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